1,945 research outputs found
Inhomogenous loop quantum cosmology with matter
The linearly polarized Gowdy model with a massless scalar field with
the same symmetries as the metric is quantized by applying a hybrid approach.
The homogeneous geometry degrees of freedom are loop quantized, fact which
leads to the resolution of the cosmological singularity, while a Fock
quantization is employed for both matter and gravitational inhomogeneities.
Owing to the inclusion of the massless scalar field this system allows us to
modelize flat Friedmann-Robertson-Walker cosmologies filled with
inhomogeneities propagating in one direction. It provides a perfect scenario to
study the quantum back-reaction between the inhomogeneities and the polymeric
homogeneous and isotropic background.Comment: 4 pages, Contribution to the proceedings of the Loops 11-Madrid
conferenc
Inclusion of matter in inhomogeneous loop quantum cosmology
We study the hybrid quantization of the linearly polarized Gowdy model
with a massless scalar field with the same symmetries as the metric. For
simplicity, we quantize its restriction to the model with local rotational
symmetry. Using this hybrid approach, the homogeneous degrees of freedom of the
geometry are quantized \`a la loop, leading to the resolution of the
cosmological singularity. A Fock quantization is employed both for the matter
and the gravitational inhomogeneities. Owing to the inclusion of the massless
scalar field this system allows us to modelize flat Friedmann-Robertson-Walker
cosmologies filled with inhomogeneities propagating in one direction, providing
a perfect scenario to study the quantum back-reaction of the inhomogeneities on
the polymeric homogeneous and isotropic background.Comment: 4 pages. Contribution to the Proceedings of Spanish Relativity
Meeting ERE2011, Madrid 201
Time-dependent mass of cosmological perturbations in the hybrid and dressed metric approaches to loop quantum cosmology
Loop quantum cosmology has recently been applied in order to extend the
analysis of primordial perturbations to the Planck era and discuss the possible
effects of quantum geometry on the cosmic microwave background. Two approaches
to loop quantum cosmology with admissible ultraviolet behavior leading to
predictions that are compatible with observations are the so-called hybrid and
dressed metric approaches. In spite of their similarities and relations, we
show in this work that the effective equations that they provide for the
evolution of the tensor and scalar perturbations are somewhat different. When
backreaction is neglected, the discrepancy appears only in the time- dependent
mass term of the corresponding field equations. We explain the origin of this
difference, arising from the distinct quantization procedures. Besides, given
the privileged role that the big bounce plays in loop quantum cosmology, e.g.
as a natural instant of time to set initial conditions for the perturbations,
we also analyze the positivity of the time-dependent mass when this bounce
occurs. We prove that the mass of the tensor perturbations is positive in the
hybrid approach when the kinetic contribution to the energy density of the
inflaton dominates over its potential, as well as for a considerably large
sector of backgrounds around that situation, while this mass is always
nonpositive in the dressed metric approach. Similar results are demonstrated
for the scalar perturbations in a sector of background solutions that includes
the kinetically dominated ones; namely, the mass then is positive for the
hybrid approach, whereas it typically becomes negative in the dressed metric
case. More precisely, this last statement is strictly valid when the potential
is quadratic for values of the inflaton mass that are phenomenologically
favored.Comment: 16 pages, 3 figures. Version to be published in PR
Approximation methods in Loop Quantum Cosmology: From Gowdy cosmologies to inhomogeneous models in Friedmann-Robertson-Walker geometries
We develop approximation methods in the hybrid quantization of the Gowdy
model with linear polarization and a massless scalar field, for the case of
three-torus spatial topology. The loop quantization of the homogeneous
gravitational sector of the Gowdy model (according to the improved dynamics
prescription) and the presence of inhomogeneities lead to a very complicated
Hamiltonian constraint. Therefore, the extraction of physical results calls for
the introduction of well justified approximations. We first show how to
approximate the homogeneous part of the Hamiltonian constraint, corresponding
to Bianchi I geometries, as if it described a Friedmann-Robertson-Walker (FRW)
model corrected with anisotropies. This approximation is valid in the
high-energy sector of the FRW geometry (concerning its contribution to the
constraint) and for anisotropy profiles that are sufficiently smooth. In
addition, for certain families of states associated to regimes of physical
interest, with negligible effects of the anisotropies and small
inhomogeneities, one can approximate the Hamiltonian constraint of the
inhomogeneous system by that of an FRW geometry with a relatively simple matter
content, and then obtain its solutions.Comment: 20 pages, 3 figures. Minor changes, matches published versio
The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology
We investigate the role played by the vacuum of the primordial fluctuations
in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton
potential is a mass term and the unperturbed quantum geometry is governed by
the effective dynamics of Loop Quantum Cosmology. In this situation, the
phenomenologically interesting solutions have a preinflationary regime where
the kinetic energy of the inflaton dominates over the potential. For these kind
of solutions, we show that the primordial power spectra depend strongly on the
choice of vacuum. We study in detail the case of adiabatic states of low order
and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all
imposed at the bounce. The adiabatic spectra are typically suppressed at large
scales, and display rapid oscillations with an increase of power at
intermediate scales. In the non-oscillating vacuum, there is power suppression
for large scales, but the rapid oscillations are absent. We argue that the
oscillations are due to the imposition of initial adiabatic conditions in the
region of kinetic dominance, and that they would also be present in General
Relativity. Finally, we discuss the sensitivity of our results to changes of
the initial time and other data of the model.Comment: 29 pages, 13 figure
Uniqueness of the Fock quantization of scalar fields under mode preserving canonical transformations varying in time
We study the Fock quantization of scalar fields of Klein-Gordon type in
nonstationary scenarios propagating in spacetimes with compact spatial
sections, allowing for different field descriptions that are related by means
of certain nonlocal linear canonical transformations that depend on time. More
specifically, we consider transformations that do not mix eigenmodes of the
Laplace-Beltrami operator, which are supposed to be dynamically decoupled. In
addition, we assume that the canonical transformations admit an asymptotic
expansion for large eigenvalues (in norm) of the Laplace-Beltrami operator in
the form of a series of half integer powers. Canonical transformations of this
kind are found in the study of scalar perturbations in inflationary
cosmologies, relating for instance the physical degrees of freedom of these
perturbations after gauge fixing with gauge invariant canonical pairs of
Bardeen quantities. We characterize all possible transformations of this type
and show that, independently of the initial field description, the combined
criterion of requiring (i) invariance of the vacuum under the spatial
symmetries and (ii) a unitary implementation of the dynamics, leads to a unique
equivalence class of Fock quantizations, all of them related by unitary
transformations. This conclusion provides even further robustness to the
validity of the proposed criterion, completing the results that have already
appeared in the literature about the uniqueness of the Fock quantization under
changes of field description when one permits exclusively local time dependent
canonical transformations that scale the field configuration.Comment: 12 pages, submitted to Phys. Rev.
Massless scalar field in de Sitter spacetime: unitary quantum time evolution
We prove that, under the standard conformal scaling, a massless field in de
Sitter spacetime admits an O(4)-invariant Fock quantization such that time
evolution is unitarily implemented. This result disproves previous claims in
the literature. We discuss the relationship between this quantization with
unitary dynamics and the family of O(4)-invariant Hadamard states given by
Allen and Folacci, as well as with the Bunch-Davies vacuum.Comment: 23 pages. Typos corrected, matches published versio
Future weak lensing constraints in a dark coupled universe
Coupled cosmologies can predict values for the cosmological parameters at low
redshifts which may differ substantially from the parameters values within
non-interacting cosmologies. Therefore, low redshift probes, as the growth of
structure and the dark matter distribution via galaxy and weak lensing surveys
constitute a unique tool to constrain interacting dark sector models. We focus
here on weak lensing forecasts from future Euclid and LSST-like surveys
combined with the ongoing Planck cosmic microwave background experiment. We
find that these future data could constrain the dimensionless coupling to be
smaller than a few . The coupling parameter is strongly
degenerate with the cold dark matter energy density and the
Hubble constant .These degeneracies may cause important biases in the
cosmological parameter values if in the universe there exists an interaction
among the dark matter and dark energy sectors.Comment: 8 pages, 6 figure
Unitary evolution and uniqueness of the Fock quantization in flat cosmologies with compact spatial sections
We study the Fock quantization of scalar fields with a time dependent mass in
cosmological scenarios with flat compact spatial sections. This framework
describes physically interesting situations like, e.g., cosmological
perturbations in flat Friedmann-Robertson-Walker spacetimes, generally
including a suitable scaling of them by a background function. We prove that
the requirements of vacuum invariance under the spatial isometries and of a
unitary quantum dynamics select (a) a unique canonical pair of field variables
among all those related by time dependent canonical transformations which scale
the field configurations, and (b) a unique Fock representation for the
canonical commutation relations of this pair of variables. Though the proof is
generalizable to other compact spatial topologies in three or less dimensions,
we focus on the case of the three-torus owing to its relevance in cosmology,
paying a especial attention to the role played by the spatial isometries in the
determination of the representation.Comment: 23 pages. New section 4.2. Added references. Published in EJT
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